Huwebes, Marso 17, 2016

A "delta" connected transformer winding is connected between phases of a three-phase system. A "wye" ("star") transformer connects each winding from a phase wire to a common neutral point.

 The material presented so far in this chapter has dealt exclusively with single-phase AC power, that is, with single sinusoidal sources. In fact, most of the AC power used today is generated and distributed as three-phase power, by means of an arrangement in which three sinusoidal voltages are generated out of phase with one another. The primary reason is efficiency: The weight of the conductors and other components in a three-phase system is much lower than that in a single-phase system delivering the same amount of power. Further, while the power produced by a single-phase system has a pulsating nature (recall the results of Section 7.1), a three-phase system can deliver a steady, constant supply of power. For example, later in this section it will be shown that a three-phase generator producing three balanced voltages—that is, voltages of equal amplitude and frequency displaced
V_1 = V_\text{LN}\angle 0^\circ,

V_2 = V_\text{LN}\angle{-120}^\circ,
V_3 = V_\text{LN}\angle{+120}^\circ.

Wye

I_1 = \frac{V_1}{|Z_\text{total}|}\angle (-\theta),
I_2 = \frac{V_2}{|Z_\text{total}|}\angle (-120^\circ - \theta),
I_3 = \frac{V_3}{|Z_\text{total}|}\angle (120^\circ - \theta),

I_1 + I_2 + I_3 = I_\text{N} = 0.

Delta

\begin{align} V_{12} &= V_1 - V_2 = (V_\text{LN}\angle 0^\circ) - (V_\text{LN}\angle {-120}^\circ) \\ &= \sqrt{3}V_\text{LN}\angle 30^\circ = \sqrt{3}V_{1}\angle (\phi_{V_1} + 30^\circ), \\ V_{23} &= V_2 - V_3 = (V_\text{LN}\angle {-120}^\circ) - (V_\text{LN}\angle 120^\circ) \\ &= \sqrt{3}V_\text{LN}\angle {-90}^\circ = \sqrt{3}V_{2}\angle (\phi_{V_2} + 30^\circ), \\ V_{31} &= V_3 - V_1 = (V_\text{LN}\angle 120^\circ) - (V_\text{LN}\angle 0^\circ) \\ &= \sqrt{3}V_\text{LN}\angle 150^\circ = \sqrt{3}V_{3}\angle (\phi_{V_3} + 30^\circ). \\ \end{align}

I_{12} = \frac{V_{12}}{|Z_\Delta|} \angle (30^\circ - \theta),
I_{23} = \frac{V_{23}}{|Z_\Delta|} \angle (-90^\circ - \theta),
I_{31} = \frac{V_{31}}{|Z_\Delta|} \angle (150^\circ - \theta),

Single-phase loads

V_\text{LL} = \sqrt{3} V_\text{LN}.



With Dennis James Matildo
3/5/16

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